20 papers · ranked by Valyu relevance
Anton Rodomanov, Yurii Nesterov
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of…
Moslem Zamani, François Glineur
We first introduce a proof technique that generalizes the standard analysis of subgradient methods. It is based on tracking the distance between the current iterate and a different reference point at each iteration. Using this technique, we obtain the exact worst-case convergence rate for the objective accuracy of the…
Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee, Courtney Paquette
'Courtney Paquette'] Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are initialized within a fixed tube around the solution set. A…
Yaohua Hu, Jiawen Li, Carisa Kwok Wai Yu
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we investigate the iteration complexity and convergence rates of various subgradient methods…
Xiao Li, Lei Zhao, Daoli Zhu, Anthony Man–Cho So
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this algorithm are mainly derived for Lipschitz continuous objective functions. In this work, we first extend the typical complexity results for the subgradient…
Kiyuob Jung, Jehan Oh
Root-Linear Convergence Authors: ['Kiyuob Jung' 'Jehan Oh'] In this paper, we find the special case of the subgradient method minimizing a one-dimensional real-valued function, which we term the specular gradient method, that converges root-linearly without any additional assumptions except the convexity. Furthermore…
Yijie Wang, Xiaoning Qian
Functional module identification in biological networks may provide new insights into the complex interactions among biomolecules for a better understanding of cellular functional organization. Most of existing functional module identification methods are based on the optimization of network modularity and cluster…
Bicheng Ying, Ali H. Sayed
—In this work and the supporting Part II [2], we examine the performance of stochastic sub-gradient learning strategies under weaker conditions than usually considered in the literature. The new conditions are shown to be automatically satisfied by several important cases of interest including SVM, LASSO, and…
Q-L Dong, A Gibali, D Jiang, Y Tang
In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving a variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning…
Kazuhiro Hishinuma, Hideaki Iiduka
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning algorithms incorporating the line search method, which automatically and…
Songnian He, Tao Wu
In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections…
Natsuki Akaishi, Koki Yamada, Kohei Yatabe, Yuki Takayama + 1 more
'A. Borbély'] This paper proposes a phase-retrieval algorithm for X-ray ptychography with almost the same computational efficiency as the conventional methods. It exploits an optimization technique, subgradient projection, which has an interesting property that means it can be expected to avoid yielding poor images.
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Kazunori D Yamada
In the deep learning era, a gradient descent method is the most common method to optimize parameters of neural networks. Among various mathematical optimization methods, a gradient descent method is the most naive method. Although controlling a learning rate of the method is necessary for quick convergence, the…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Michael Cho + 2 more
High dimensional linear regression problems are often fitted using LASSO-type approaches. Although the LASSO objective function is convex, it is not differentiable everywhere, making the use of gradient descent methods for minimization not straightforward. To avoid this technical issue, we apply Nesterov smoothing to…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Christoph Lange
Penalized linear regression approaches that include an L_1_ term have become an important tool in statistical data analysis. One prominent example is the least absolute shrinkage and selection operator (Lasso), though the class of L_1_ penalized regression operators also includes the fused and graphical Lasso, the…
Authors not listed
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
Maxwell W. Libbrecht, Jeffrey A. Bilmes, William Stafford Noble
Submodular optimization, a discrete analogue to continuous convex optimization, has been used with great success in many fields but is not yet widely used in biology. We apply submodular optimization to the problem of removing redundancy in protein sequence data sets. This is a common step in many bioinformatics and…
Christoph Jacob, Johannes Neugebauer
The past years since the publication of our review on subsystem density-functional theory (sDFT) [WIREs Comput. Mol. Sci. 2014, 4:325--362] have witnessed a rapid development and diversification of quantum mechanical fragmentation and embedding approaches related to sDFT and frozen-density embedding (FDE). In this…